If an image contains two distinct objects, should I create a copy of this image with distinct labels for each copy?
You should use both classes together. Let's say you use the method you proposed. Then they will be contradicting each other as one teaches the network to recognize people, not objects and the other teaches the network to recognizes objects not person. There is no need for seperation of the two classes, unless you are making two seperate classifier. Hope I can help you.